{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src=\"http://hilpisch.com/tpq_logo.png\" alt=\"The Python Quants\" width=\"35%\" align=\"right\" border=\"0\"><br>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Derivatives Analytics with Python"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**_Chapter 8_**\n",
    "\n",
    "**Wiley Finance (2015)**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src=\"http://hilpisch.com/images/derivatives_analytics_front.jpg\" alt=\"Derivatives Analytics with Python\" width=\"30%\" align=\"left\" border=\"0\">"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Dr. Yves J. Hilpisch\n",
    "\n",
    "The Python Quants GmbH\n",
    "\n",
    "<a href='mailto:dawp@tpq.io'>dawp@tpq.io</a> | <a href='http://tpq.io'>http://tpq.io</a>\n",
    "\n",
    "Python online training | <a href='http://training.tpq.io'>http://training.tpq.io</a>\n",
    "\n",
    "DX Analytics library | <a href='http://dx-analytics.com'>http://dx-analytics.com</a>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from pylab import plt\n",
    "plt.style.use('seaborn')\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Valuation by Integration & FFT"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Value of Call Option   19.948\n"
     ]
    }
   ],
   "source": [
    "%run 08_m76/M76_valuation_INT.py"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Value of Call Option   19.948\n"
     ]
    }
   ],
   "source": [
    "%run 08_m76/M76_valuation_FFT.py"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Calibration to 3 Maturities"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   0 | [0.075 0.100 -0.500 0.100] |  35.009 |  35.009\n",
      "  50 | [0.075 0.300 -0.100 0.200] |  34.892 |  12.884\n",
      " 100 | [0.100 0.200 -0.200 0.100] |  24.976 |   9.283\n",
      " 150 | [0.125 0.100 -0.400 0.300] |   9.822 |   7.415\n",
      " 200 | [0.125 0.400 -0.500 0.200] |  53.397 |   5.581\n",
      " 250 | [0.150 0.200 0.000 0.100] |   5.022 |   3.822\n",
      " 300 | [0.175 0.100 -0.200 0.300] |  18.181 |   3.822\n",
      " 350 | [0.175 0.400 -0.300 0.200] |  46.957 |   3.822\n",
      " 400 | [0.200 0.300 -0.400 0.100] |  61.238 |   3.822\n",
      " 450 | [0.150 0.095 -0.206 0.198] |   3.798 |   3.798\n",
      " 500 | [0.160 0.008 -0.282 0.097] |   3.585 |   3.584\n",
      " 550 | [0.160 0.004 -0.273 0.113] |   3.584 |   3.584\n",
      " 600 | [0.160 0.005 -0.271 0.118] |   3.584 |   3.584\n",
      " 650 | [0.160 0.004 -0.286 0.118] |   3.584 |   3.584\n",
      " 700 | [0.160 0.003 -0.446 0.121] |   3.584 |   3.584\n",
      " 750 | [0.160 0.002 -0.611 0.112] |   3.583 |   3.583\n",
      " 800 | [0.160 0.001 -1.035 0.143] |   3.583 |   3.583\n",
      " 850 | [0.160 0.001 -1.469 0.193] |   3.583 |   3.583\n",
      " 900 | [0.160 0.001 -2.480 0.322] |   3.583 |   3.583\n",
      " 950 | [0.160 0.001 -4.268 0.563] |   3.583 |   3.583\n",
      "1000 | [0.160 0.001 -7.224 0.963] |   3.583 |   3.583\n",
      "1050 | [0.160 0.001 -16.274 2.190] |   3.583 |   3.583\n",
      "1100 | [0.160 0.001 -21.307 2.872] |   3.583 |   3.583\n",
      "1150 | [0.160 0.001 -30.691 4.145] |   3.583 |   3.583\n",
      "Warning: Maximum number of function evaluations has been exceeded.\n",
      "CPU times: user 36.5 s, sys: 426 ms, total: 36.9 s\n",
      "Wall time: 37.1 s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "%run 08_m76/M76_calibration_FFT.py"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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PfvQHzinqSSJSS0T65NlUA/gOWI11yQigafCxUqVOaiqMHu1h/Xpr4dfixUk0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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10b5010b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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AMu3aOdm2TVd8UxVTMEnhZxHJynkgIl7gQOhCUiq6OJ0wZEgm27al0bWrl88/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\nVbGttUm9kTsAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10b768e10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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WrUqiZUs3U6c68HqDyziXZpGW0Zy6J6aRltEc59Ks2Aat1FGwBY5wl44x5j4g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\nSYuCUqpGq10bhg718dFHuXT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      "text/plain": [
       "<matplotlib.figure.Figure at 0x10b7176a0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "generate_plot(opt, options);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Calibration to Short Maturity"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   0 | [0.100 0.100 -0.400 0.000] |  13.102 |  13.102\n",
      "  50 | [0.100 0.200 -0.200 0.000] |  13.074 |  10.498\n",
      " 100 | [0.100 0.300 0.000 0.020] |  15.648 |   7.988\n",
      " 150 | [0.100 0.500 -0.300 0.040] |   6.087 |   4.338\n",
      " 200 | [0.100 0.600 -0.100 0.060] |  12.132 |   4.338\n",
      " 250 | [0.125 0.100 -0.400 0.080] |   9.119 |   4.014\n",
      " 300 | [0.125 0.200 -0.200 0.100] |   9.139 |   4.014\n",
      " 350 | [0.125 0.300 0.000 0.120] |  10.455 |   3.779\n",
      " 400 | [0.125 0.500 -0.200 0.000] |   5.123 |   1.560\n",
      " 450 | [0.125 0.600 0.000 0.020] |  11.610 |   1.352\n",
      " 500 | [0.150 0.100 -0.300 0.040] |   6.047 |   1.352\n",
      " 550 | [0.150 0.200 -0.100 0.060] |   6.874 |   1.352\n",
      " 600 | [0.150 0.400 -0.400 0.080] |   3.860 |   1.352\n",
      " 650 | [0.150 0.500 -0.200 0.100] |   2.776 |   1.352\n",
      " 700 | [0.150 0.600 0.000 0.120] |   6.279 |   1.352\n",
      " 750 | [0.175 0.100 -0.200 0.000] |   5.391 |   1.352\n",
      " 800 | [0.175 0.200 0.000 0.020] |   5.842 |   1.352\n",
      " 850 | [0.175 0.400 -0.300 0.040] |   7.156 |   1.352\n",
      " 900 | [0.175 0.500 -0.100 0.060] |   5.342 |   1.352\n",
      " 950 | [0.175 0.700 -0.400 0.080] |  16.331 |   1.352\n",
      "1000 | [0.200 0.100 -0.200 0.100] |   8.506 |   1.352\n",
      "1050 | [0.200 0.200 0.000 0.120] |   8.725 |   1.352\n",
      "1100 | [0.200 0.400 -0.200 0.000] |  10.600 |   1.352\n",
      "1150 | [0.200 0.500 0.000 0.020] |   8.135 |   1.352\n",
      "1200 | [0.200 0.700 -0.300 0.040] |  17.515 |   1.352\n",
      "1250 | [0.130 0.587 -0.276 0.131] |   0.963 |   0.950\n",
      "1300 | [0.130 0.716 -0.227 0.124] |   0.923 |   0.916\n",
      "1350 | [0.130 0.894 -0.184 0.104] |   0.886 |   0.881\n",
      "1400 | [0.125 1.350 -0.138 0.015] |   0.613 |   0.599\n",
      "1450 | [0.124 1.390 -0.137 0.000] |   0.579 |   0.579\n",
      "1500 | [0.124 1.393 -0.137 0.000] |   0.579 |   0.579\n",
      "1550 | [0.124 1.393 -0.137 0.000] |   0.579 |   0.579\n",
      "Optimization terminated successfully.\n",
      "         Current function value: 0.578880\n",
      "         Iterations: 239\n",
      "         Function evaluations: 403\n",
      "CPU times: user 42.7 s, sys: 397 ms, total: 43.1 s\n",
      "Wall time: 43.2 s\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.figure.Figure at 0x108a5cc18>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%%time\n",
    "%run 08_m76/M76_calibration_single.py"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.124, 1.393, -0.137, 0.000])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "opt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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4unSJMGdONWeeGVsc8Kij/Nx1lxYHFBERWZ+sKXDMrBdwBrCtmV1jZs2BkJmNM7OrgdOA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\ntpWISCNJR4FzlnP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hppt87LtvCRdd1Izv7niK0l5dweultFdXfFMmZzpskbymAkdEJIXM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\nkiRVzv8BiXY2WiOizKkAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10c0880f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "generate_plot(opt, options);\n",
    "plt.savefig('../images/08_m76/M76_calibration_single.pdf')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Monte Carlo Simulation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Value of Call Option  119.360\n",
      "CALL STRIKE         3000.000\n",
      "----------------------------\n",
      "Call Value by Int    273.875\n",
      "Call Value by FFT    273.856\n",
      "Difference FFT/Int    -0.018\n",
      "Call Value by MCS    274.741\n",
      "Difference MCS/Int     0.867\n",
      "----------------------------\n",
      "CALL STRIKE         3050.000\n",
      "----------------------------\n",
      "Call Value by Int    235.371\n",
      "Call Value by FFT    235.366\n",
      "Difference FFT/Int    -0.005\n",
      "Call Value by MCS    236.215\n",
      "Difference MCS/Int     0.844\n",
      "----------------------------\n",
      "CALL STRIKE         3100.000\n",
      "----------------------------\n",
      "Call Value by Int    198.942\n",
      "Call Value by FFT    198.955\n",
      "Difference FFT/Int     0.013\n",
      "Call Value by MCS    199.739\n",
      "Difference MCS/Int     0.797\n",
      "----------------------------\n",
      "CALL STRIKE         3150.000\n",
      "----------------------------\n",
      "Call Value by Int    164.918\n",
      "Call Value by FFT    164.940\n",
      "Difference FFT/Int     0.022\n",
      "Call Value by MCS    165.654\n",
      "Difference MCS/Int     0.736\n",
      "----------------------------\n",
      "CALL STRIKE         3200.000\n",
      "----------------------------\n",
      "Call Value by Int    133.699\n",
      "Call Value by FFT    133.715\n",
      "Difference FFT/Int     0.016\n",
      "Call Value by MCS    134.354\n",
      "Difference MCS/Int     0.654\n",
      "----------------------------\n",
      "CALL STRIKE         3250.000\n",
      "----------------------------\n",
      "Call Value by Int    105.703\n",
      "Call Value by FFT    105.702\n",
      "Difference FFT/Int    -0.001\n",
      "Call Value by MCS    106.254\n",
      "Difference MCS/Int     0.552\n",
      "----------------------------\n",
      "CALL STRIKE         3300.000\n",
      "----------------------------\n",
      "Call Value by Int     81.280\n",
      "Call Value by FFT     81.263\n",
      "Difference FFT/Int    -0.017\n",
      "Call Value by MCS     81.696\n",
      "Difference MCS/Int     0.416\n",
      "----------------------------\n",
      "CALL STRIKE         3350.000\n",
      "----------------------------\n",
      "Call Value by Int     60.644\n",
      "Call Value by FFT     60.621\n",
      "Difference FFT/Int    -0.023\n",
      "Call Value by MCS     60.936\n",
      "Difference MCS/Int     0.292\n",
      "----------------------------\n",
      "CALL STRIKE         3400.000\n",
      "----------------------------\n",
      "Call Value by Int     43.813\n",
      "Call Value by FFT     43.799\n",
      "Difference FFT/Int    -0.015\n",
      "Call Value by MCS     43.973\n",
      "Difference MCS/Int     0.160\n",
      "----------------------------\n",
      "CALL STRIKE         3450.000\n",
      "----------------------------\n",
      "Call Value by Int     30.601\n",
      "Call Value by FFT     30.603\n",
      "Difference FFT/Int     0.002\n",
      "Call Value by MCS     30.671\n",
      "Difference MCS/Int     0.070\n",
      "----------------------------\n",
      "CALL STRIKE         3500.000\n",
      "----------------------------\n",
      "Call Value by Int     20.639\n",
      "Call Value by FFT     20.657\n",
      "Difference FFT/Int     0.018\n",
      "Call Value by MCS     20.678\n",
      "Difference MCS/Int     0.039\n",
      "----------------------------\n",
      "CALL STRIKE         3550.000\n",
      "----------------------------\n",
      "Call Value by Int     13.438\n",
      "Call Value by FFT     13.461\n",
      "Difference FFT/Int     0.023\n",
      "Call Value by MCS     13.472\n",
      "Difference MCS/Int     0.034\n",
      "----------------------------\n",
      "CALL STRIKE         3600.000\n",
      "----------------------------\n",
      "Call Value by Int      8.449\n",
      "Call Value by FFT      8.465\n",
      "Difference FFT/Int     0.016\n",
      "Call Value by MCS      8.488\n",
      "Difference MCS/Int     0.039\n",
      "----------------------------\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10ab33a20>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%run 08_m76/M76_valuation_MCS.py"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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Kza25l6XI3lLP4ZlnoH17uOoqFwMHZvHZZ1k88wzUTFBr1HPnqefOU8+dp56n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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10c184eb8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "results.plot(style=['b-', 'g^', 'ro'], figsize=(10, 6))\n",
    "plt.ylabel('option value')\n",
    "plt.savefig('../images/08_m76/M76_value_comparison.pdf')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src=\"http://hilpisch.com/tpq_logo.png\" alt=\"The Python Quants\" width=\"35%\" align=\"right\" border=\"0\"><br>\n",
    "\n",
    "<a href=\"http://tpq.io\" target=\"_blank\">http://tpq.io</a> | <a href=\"http://twitter.com/dyjh\" target=\"_blank\">@dyjh</a> | <a href=\"mailto:training@tpq.io\">training@tpq.io</a>\n",
    "\n",
    "**Quant Platform** |\n",
    "<a href=\"http://quant-platform.com\">http://quant-platform.com</a>\n",
    "\n",
    "**Python for Finance** |\n",
    "<a href=\"http://python-for-finance.com\" target=\"_blank\">Python for Finance @ O'Reilly</a>\n",
    "\n",
    "**Derivatives Analytics with Python** |\n",
    "<a href=\"http://derivatives-analytics-with-python.com\" target=\"_blank\">Derivatives Analytics @ Wiley Finance</a>\n",
    "\n",
    "**Listed Volatility and Variance Derivatives** |\n",
    "<a href=\"http://lvvd.tpq.io\" target=\"_blank\">Listed VV Derivatives @ Wiley Finance</a>\n",
    "\n",
    "**Python Online Training** |\n",
    "<a href=\"http://certificate.tpq.io\" target=\"_blank\">Python for Algorithmic Trading University Certificate</a>"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}
